Felipe Caicedo, second left, who is on loan from Manchester City, has scored a remarkable 10 goals from only 23 shots. Photograph: Kai Foersterling/EPA

They might as well have been an 18-stone heifer puffing their way down the High Road in an unappealingly tight top with "Babe" stretched across the chest. Or "Supermodel". It was the final weekend in January and UD Levante took to the field at the Ciutat de València stadium wearing T-shirts made especially for the occasion, pulled on over their kits and with a message to convey. La unión es salvación; gracias, afición: "union is salvation," they said on the front; "thanks, fans," they said on the back. Levante's players lined up and applauded the supporters. And then Levante's supporters applauded them back.

All 10,500 of them.

10,500 was the lowest attendance of the day and it was no one-off: as a percentage of their ground's capacity Levante have the lowest average support in the First Division – even though the stadium holds only 25,000. And as for salvation, that looked impossible. Promoted last season, Levante were bottom and seemed set to stay there.

They'd not won a league match in 2011 and had lost five in a row – lose one more and they'd complete the second worst record run in history, their early-season draw with Real Madrid long forgotten. Sure, they'd recently beaten Madrid in the Copa del Rey – but only because Madrid had beaten them in the first leg. Eight-nil.

You couldn't really expect more. Recently out of administration, Levante have the league's smallest budget: Madrid spend more on Cristiano Ronaldo than they do on everyone. Their top earner makes only €350,000 a year and their coach couldn't switch on the ProZone because it costs too much. They'd signed 12 players in the summer for a total of €0m and over 30 players in three years for the same amount. They had the oldest defence since "Sorry, I slipped" and their sporting director admitted having built a squad from cast-offs, packing the team with vaguely familiar faces you mostly didn't rate much in the first place – blasts from a not particularly glorious past. A kind of footballing The Expendables.

In short, they were doomed. Just wearing a T-shirt doesn't make it so. Instead it brings to mind one of the most telling Spanish phrases: dime de lo que presumes y te diré de que careces. Tell me what you boast of and I'll tell you what you lack.

Not this time. She might have been bloody well hidden but there really was a supermodel squeezed in there. Union might be salvation – implausible though it appeared, Levante were right to thank their fans and right to wear the T-shirts. That day, they beat Getafe 2-0. Then they defeated Villarreal 1-0. And then they beat Almería 1-0. "Winning three on the trot is quite a feat," said the coach, Luis García, but there was more to come. They were defeated 2-0 by Real Madrid at the Bernabéu but as García noted: "this isn't our war". Osasuna, on the other hand, certainly is their war. And on Sunday evening, Sergio Ballesteros bundled over the line and Felipe Caicedo raced on to a long, quick-witted punt from goalkeeper Gustavo Munúa to give Levante a 2-1 win against Osasuna.

Not just a 2-1 win but a deserved 2-1 win – "Levante," said the Osasuna coach José Luis Mendilibar, "were the better team" — a two-point lead and a now-unassailable goal advantage in head-to-head goal difference. Better still, a 2-1 win that means Osasuna are now one of four teams between Levante and the relegation zone.

It is quite a turnaround. The team that had won only four times in 20 weeks have now won as many times in five. At the end of January Levante were bottom; at the end of February they are seven points off the bottom (although Málaga play on Monday night), three off the relegation zone and all the way up in 13th. Luis García reckons 38 points will clinch survival this season — get as many points in their final 13 games as they have in their last five and Levante will be safe. "They're alive!" shouted the headline on the day Levante defeated Getafe. Now, they most certainly are.

Maybe they always were. Maybe we were the only ones that didn't believe in them; they certainly believed in themselves. Early this year, García called a meeting with his dressing room heavyweights [insert your own Ballesteros joke here] and together they discussed the way forward. The conclusions were clear: Levante knew their limitations but if they know they're not that good they also knew they weren't that bad.

They had been beaten 4-1 by Sevilla but it was usually the odd goal – sometimes the very odd goal – that did for them. They were beaten narrowly 2-1 at the Camp Nou, the second best result anyone has got there all season. They lost the city derby 1-0 to an 83rd-minute goal from a suspiciously offside-looking Juan Mata. Real Zaragoza beat them 1-0 in the thick fog, with Levante having a goal ruled out for no apparent reason and their coach handed a two-match ban for the heinous crime of shouting "that's a goal! that's a goal!". And Athletic Bilbao defeated them 2-1 through two set plays, with Caicedo missing a last-minute chance that left García tearing off his scarf and throwing it down in frustration.

Levante kept the faith. Unity is salvation. On the pitch and in the stands. As Ballesteros puts it their fans may be few but they are "very, very loyal and very loud." Their players might not be superstars, but they are committed and, given the financial limitations, the squad is genuinely not bad – a miracle of construction on the cheap.

Ballesteros has a reputation for being a hardman, even though as he quite correctly points out, in a voice that is surprisingly soft and measured for a beast of a man with a neck like an ox, he actually commits fewer than a foul a game. What he is, though, is clever and extremely competitive, marshalling a tight, well-organised defence. Munúa has given them greater solidity in goal. Juanlu never, ever stops running. Xavi Torres holds the midfield. And Caicedo, one-time winner of Ecuador's equivalent of Football Idol and on loan from Manchester City with a €1m option to buy, is a battering ram of a striker – fast, strong and deadly. He has scored 10 goals in only 14 games. Even more ridiculously, he has 10 goals from 23 shots, the most effective striker in Primera.

That's just one example of García getting the best out of his squad. Now in his third year at the club, a former Atlético Madrid fan and player who never quite made it, getting called into the squad but never on to the pitch, García still lives alone in a city hotel – room 1502 – and admits that he has a lot in common with Rafa Benítez in his meticulousness. Levante have the worst pass-completion statistics in the division. They attempt the second fewest, too. Recognising their technical weaknesses, they are direct, quick to get the ball into the area, rapid on the break and ready to commit men when they do spring forward, Juanlu and Caicedo especially – they are the league's third most productive assist-goal partnership. Meanwhile, only six teams have scored fewer than them but only five have scored more from set plays.

And yet if García is like Benítez in that sense, he could hardly be less like him in others. "If the players aren't happy, no system works," he says. Smart, passionate and eloquent, the youngest coach in the division at 38, his greatest talent is for motivation. Solidarity is his thing. Everything Levante do is done collectively, the tasks shared. Even fouling: only four teams have more yellow cards than Levante but they do not have a single player in the top 20. An experienced, bright, intelligent squad of players helps; one that has been made aware of their significance to fans who feared the club disappearing two years ago. "This an honest, grounded group," says Ballesteros, "and we're very conscious of what being in the First Division means".

It is also a united one. "The manager's psychological work is extremely important," Ballesteros says. "He is very inventive." In the corridor from the dressing room to the pitch at the Ciutat de València, the walls are painted red and blue, embossed with pictures of their fans. Over the top are slogans, warning and motivation wrapped into one: "A history to honour, a future to conquer", "You come here to play: you may win, but you will suffer." Newspaper cuttings from their victories are papered on to the walls of the dressing room and videos of their goals are played on the team bus. Before one recent game, García opened a box that had been sitting, sealed, in the dressing room all week. Inside were pieces of paper with messages written by fans who, unbeknownst to the players, had been given access to the stadium during the previous seven days. One by one, they read them out: messages of encouragement and togetherness.

"The players have to know that the man alongside them is a compañero, a brother," García says. It does not matter how hard the task, strength comes in unity. One training session he has employed features blindfolded games in which a player's only guide is the team-mate talking them through every move, while on the way to Villarreal, García showed a video of Team Hoyte, the father and son iron man triathlon, marathon and endurance pair with a difference – Dick Hoyte runs, swims and cycles carrying his son Rick, who suffers from cerebral palsy, with him every inch of the way.

Earlier this season, Luis García made his players climb a wall at the club's training ground. Standing at the top, they had to shut their eyes and let themselves fall backwards into the waiting arms of their team-mates. At first, they were convinced they were going down. Now they're convinced they're not.

Week 25 results and talking points:

•Dani Aranzubia: doesn't just score goals. No. This weekend he stopped them too. The Deportivo goalkeeper got back to doing what a goalkeeper is supposed to do on Saturday night – making a handful of excellent saves to stop Real Madrid at Riazor. After a dreadful first half, Madrid replaced Kaká with Ángel Di María on 60 minutes and came streaming at Deportivo in the final half-hour. Madrid have scored nought or one in five of their last seven league games but this time you could hardly blame them. (José Mourinho decided to blame the fixture list by the way: the same fixture list that will give them two days' more rest than Málaga on Thursday night). They had 21 shots, nine on target, to Deportivo's four (one) but couldn't find a way through. Cristiano Ronaldo hit the post, Emmanuel Adebayor hit the post and Aranzubia's most outstanding save came from a Di María shot. "That's football," said one headline, with a surprisingly admirable lack of whinging and whining. Madrid have now dropped points away at Osasuna, Deportivo, Mallorca, Levante and Almería – as well, of course, as at Barcelona. That said, Sergio Ramos, who lamented Madrid's failure to "take all three points" from Lyon in midweek, probably thinks 0-0 is a good result to take back to the Bernabéu for the second leg.

• Speaking of Barcelona, they're now seven points clear of Madrid again – and seven points, as Iker Casillas admitted "is a big gap". It wasn't supposed to be this way round. This was supposed to be the weekend in which the gap was cut, not the weekend in which it was lengthened. Barcelona travelled to Mallorca without Carles Puyol, Dani Alves, Victor Valdés and Xavi. And for a while it looked like it was going to be difficult, too. Then Leo Messi scored a neat header after Seydou Keita's lovely scooped pass and Barcelona took control. It was Messi's 26th league goal of the season (or 25th, or 27th depending on which website you believe: is it really that hard to count?), taking him ahead of Ronaldo. And Mallorca, Racing, Levante*, Deportivo, Hércules. Osasuna*, Sporting, Zaragoza and Almería. David Villa then got his 21st of the season – as many as Zlatan Ibrahimovic managed last season — and Pedro added the third. "Barcelona don't even give you time to foul them," sighed Michael Laudrup. "They move the ball with one or two touches and by the time you get there, it's gone. They leave you shattered." [* OK, OK, level with them]

• And the Oscar goes to ... David Navarro. The Valencia captain leapt up into the air, smacked Fernando Llorente with an elbow full in the face and then fell to the floor, dead. A stretcher came on and took him off. For a minute you thought it might actually be serious, so still was he lying, so motionless, so convincingly had his eyes rolled back in his head. You genuinely wondered about him, however much you watched the replay and confirmed your initial thought: that the sneaky cheat had not even been touched. Thirty seconds later he was running back on, having handily avoided the yellow card, everything intact. Except his credibility.

• Might Ivan Rakitic be exactly the player that Sevilla so desperately needed? At last an actual central midfielder to play in their midfield. Sevilla scored two wonderful goals but conceded two more in a fun-packed match at the Vicente Calderón with Atlético. Atlético really should have scored three as well. Javi Varas picked up a backpass (to allow treatment to an Atlético player on the ground?), the referee blew, Tiago ripped the ball out of his hands, took the free-kick quickly from nine yards out with no one anywhere near him, rolled it to Agüero, and Agüero ... missed. Varas dived at his feet and blocked the shot. Which may have been a good thing or we'd have had another scandal on our hands. A scandal that would have been the ref's fault, of course – why hold players responsible for what players do when you can blame the bastard in the black?